Context. We present the analysis of supernova remnants (SNRs) and candidates in M 31 identified in the XMM-Newton large programme survey of M 31. Supernova remnants are among the brightest X-ray sources in a galaxy. They are good indicators of the recent star-formation activities of galaxies and the interstellar environment in which they evolve. Aims. By combining the X-ray data of sources in M 31 with optical data as well as optical and radio catalogues, we aim to compile a complete, revised list of SNRs emitting X-rays in M 31 detected with XMM-Newton, study their luminosity and spatial distributions, and understand the X-ray spectra of the brightest SNRs. Methods. We analysed the X-ray spectra of the 12 brightest SNRs and candidates that have been observed with XMM-Newton. Our study of the four brightest sources allowed us to perform a more detailed spectral analysis and compare different models to describe their spectrum. For all M 31 large programme sources, we searched for their optical counterparts in the Hα, [SII], and [OIII] images of the Local Group Galaxy Survey. Results. We confirm 21 X-ray sources as counterparts to known SNRs. In addition, we identify 5 new X-ray sources as X-ray and optically emitting SNRs. Seventeen sources are no longer considered as SNR candidates. We thus create a list of 26 X-ray SNRs and 20 X-ray SNR candidates in M 31 based on their X-ray, optical, and radio emission, which is the most recent complete list of X-ray SNRs in M 31. The brightest SNRs have X-ray luminosities of up to 8 × 1036 erg s-1 in the 0.35–2.0 keV band.